Finite Group Databasebeta

← #13079839

Subgroups — #13079839

Order 1408.

362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10623010C211yesmaximal, characteristic
2C2×#66922C211yesmaximal, characteristic, complemented
3C11×#432C211yesmaximal, characteristic, complemented
4#10622463C212yesmaximal, complemented
5#10622455C212yesmaximal, complemented
6#10622349C212yesmaximal
7#10622334C212yesmaximal, complemented
8#10622327C212yesmaximal, complemented
9#10622315C212yesmaximal, complemented
10C22×Dic22—21no—
11C2×C42×C11C2211yescharacteristic
12#66983C2211yescharacteristic
13#66982—21no—
14C4×C22⋊D11—21no—
15C2×C4⋊Dic11—21no—
16C2×C4⋊Dic11C2212yes—
17#66977C2211yescharacteristic
18#66929—21no—
19#66928C2211yescharacteristic
20C4×D44C2211yescharacteristic
21#66925—21no—
22#66923C2211yescharacteristic
23#66922—21no—
24#66922—21no—
25#66922C2212yes—
26#66922C2212yes—
27C4×Dic22C2211yescharacteristic
28C11×C4⋊C8C2212yes—
29C11×C22⋊C8C2212yes—
30C11×#97C2212yes—
31#66885C2214yes—
32#66882C2214yes—
33#66881C2214yes—
34#66880C2214yes—
35C22×C4×C11D411yescharacteristic
36C22×C4×C11D411yescharacteristic
37C22×C4×C11C2311yescharacteristic
38C2×C22⋊D11—21no—
39C22×Dic11—22no—
40C2×D44C2311yescharacteristic
41C2×C4×D11—21no—
42C2×Dic22—22no—
43C2×Dic22—22no—
44C2×Dic22—44no—
45C2×Dic22C2311yescharacteristic
46C2×C8×C11C2314yes—
47C42×C11D411yescharacteristic
48C42×C11D411yescharacteristic
49C42×C11C2311yescharacteristic
50C42×C11C2311yescharacteristic
51C22⋊Dic11—21no—
52(C2×D11)⋊C4—21no—
53(C2×D11)⋊C4—21no—
54(C2×D11)⋊C4—21no—
55(C2×D11)⋊C4—21no—
56C4⋊Dic11—22no—
57C4⋊Dic11—22no—
58C4⋊Dic11—22no—
59C4⋊Dic11C2314yes—
60C4⋊Dic11C2311yescharacteristic
61C4⋊Dic11C2311yescharacteristic
62Dic11⋊C4—21no—
63Dic11⋊C4—21no—
64Dic11⋊C4—21no—
65Dic11⋊C4—21no—
66C4×Dic11—21no—
67#3238—111nomaximal, Sylow
68C23×C11C2×D411yescharacteristic
69C22×D11—21no—
70C2×C4×C11—22no—
71C2×C4×C11—22no—
72C2×C4×C11—22no—
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2×D411yescharacteristic
76C2×C4×C11C2×D411yescharacteristic
77C2×C4×C11C2×D411yescharacteristic
78C2×C4×C11C2411yescharacteristic
79C22⋊D11—42no—
80C2×Dic11—21no—
81C2×Dic11—21no—
82C2×Dic11—21no—
83C2×Dic11—24no—
84C2×Dic11—44no—
85D44—22no—
86C4×D11—42no—
87Dic22—22no—
88Dic22—44no—
89Dic22—44no—
90C8×C11—24no—
91C2×C4⋊Q8—111no—
92#529—111no—
93#501—112no—
94#489—112no—
95#483—112no—
96#480—112no—
97#477—112no—
98#476—112no—
99#432D1111yescharacteristic, complemented
100C22×C11—21no—
101C22×C11—21no—
102C22×C11AGL(1,ℤ/8)12yes—
103C22×C11C22×D411yescharacteristic
104C2×D11—41no—
105C2×D11—41no—
106C2×D11—41no—
107C4×C11—21no—
108C4×C11—21no—
109C4×C11—21no—
110C4×C11—21no—
111C4×C11#13712yes—
112C4×C112−1+412yes—
113Dic11—41no—
114Dic11—44no—
115Dic11—41no—
116Dic11—41no—
117C22×Q8—221no—
118C4⋊Q8—112no—
119C4⋊Q8—112no—
120C4⋊Q8—221no—
121C4⋊Q8—221no—
122#126—221no—
123#125—111no—
124#124—111no—
125#123—221no—
126C22⋊Q8—111no—
127#121—111no—
128C4×Q8—111no—
129C4×D4—111no—
130C4×D4—221no—
131#117—221no—
132C2×C4⋊C4—112no—
133C2×C4⋊C4—221no—
134C2×C42C2×D1111yescharacteristic
135#107—114no—
136#106—114no—
137C4⋊C8C2×D1112yes—
138#103—114no—
139#102—114no—
140C22⋊C8C2×D1112yes—
141#97C2×D1112yes—
142C2×C11—22no—
143C2×C11#53611yescharacteristic
144C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
145C2×C11C2×#13711yescharacteristic
146D11—81no—
147C2×Q8—111no—
148C2×Q8—222no—
149C2×Q8—222no—
150C2×Q8—444no—
151C2×D4—111no—
152C2×D4—221no—
153C22×C4—222no—
154C22×C4—221no—
155C22×C4D4411yescharacteristic
156C22×C4D4411yescharacteristic
157C22×C4C22×D1111yescharacteristic
158C2×C8C22×D1114yes—
159C4⋊C4—114no—
160C4⋊C4—111no—
161C4⋊C4—111no—
162C4⋊C4—222no—
163C4⋊C4—222no—
164C4⋊C4—222no—
165C4⋊C4—221no—
166C4⋊C4—221no—
167C4⋊C4—221no—
168C4⋊C4—221no—
169C22⋊C4—221no—
170C22⋊C4—221no—
171C22⋊C4—221no—
172C22⋊C4—221no—
173C22⋊C4—221no—
174C42—221no—
175C42D4411yescharacteristic
176C42D4411yescharacteristic
177C42C22×D1111yescharacteristic
178C42C22×D1111yescharacteristic
179C11#323811yescharacteristic, complemented, Sylow
180C23—221no—
181C23C2×D4411yescharacteristic
182Q8—222no—
183Q8—444no—
184Q8—444no—
185D4—222no—
186D4—442no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—221no—
191C2×C4—221no—
192C2×C4—221no—
193C2×C4—224no—
194C2×C4—444no—
195C2×C4—442no—
196C2×C4C2×D4411yescharacteristic
197C2×C4C2×D4411yescharacteristic
198C2×C4C2×D4411yescharacteristic
199C2×C4C2×D4411yescharacteristic
200C2×C4C2×D4411yescharacteristic
201C2×C4C23×D1111yescharacteristic
202C8—24no—
203C22—21no—
204C22—21no—
205C22—441no—
206C22—441no—
207C22—441no—
208C22#6696112yes—
209C22C22×D4411yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—444no—
215C4—441no—
216C4—441no—
217C4—441no—
218C4#6696212yes—
219C4#6704312yes—
220C2—22no—
221C2—881no—
222C2#1062305711yescharacteristic
223C2C2×#6696111yescharacteristic
224C2C2×#6696211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#432C2
socleC22×C11C22×D4
prime radical#66983C22
hypercenter#432D11
hypocenterC11#3238
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×#66922C2semidirect
3. C11×#432C2semidirect
4. #10622463C2semidirect
5. #10622455C2semidirect
7. #10622334C2semidirect
8. #10622327C2semidirect
9. #10622315C2semidirect
99. #432D11semidirect
179. C11#3238semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#106230102
C2×#669222
C11×#4322
#106224632
#106224552
#106223492
#106223342
#106223272
#106223152
#323811